1. Field of the Invention
The invention relates to a method for determining a set of optical imaging functions that describe the imaging of a measuring volume onto each of a plurality of detector surfaces on which the measuring volume can be imaged at in each case a different observation angle by means of detection optics, comprising the steps:                a) performing pre-calibration, during which for each detector surface the assignment of each volume position in the measuring volume to an image position on the respective detector surface is determined,        b) simultaneous imaging of the measuring volume, in which a plurality of optically detectable particles are distributed, onto the detector surfaces,        c) determining support positions, namely of the volume positions of at least a few particles, from image positions of corresponding particle images in the images of the measuring volume generated in step b by applying a triangulation method based upon the assignments determined in step a,        d) improving the assignments determined in step a by using the support positions determined in step c, so that a set of improved assignments is obtained as a set of the imaging functions to be determined.        
The invention further relates to a method for reconstructing a measuring volume with a constellation of optically detectable particles, using a plurality of two-dimensional images of the measuring volume that were recorded simultaneously at, in each case, a different observation angle on each detector surface using detector optics.
2. Description of the Related Art
A generic method for determining a set of imaging functions is known from German patent DE 10 2006 055 746 A1.
Such imaging functions are used in particular in optical methods for determining a three-dimensional velocity field of a flowing fluid in a measuring volume. Typical measuring methods of this kind are known to a person skilled in the art as PIV (Particle Imaging Velocimetry) or PTV (Particle Tracking Velocimetry). In both methods, a fluid carrying optically detectable particles is allowed to flow through a measuring volume. Typically, the particles are excited by suitable illumination to radiate light, e.g. by reflection, scattering, fluorescence, or similar. The emitted light is then transmitted via suitable detection optics simultaneously to several planar detectors on which the measuring volume is imaged, i.e. two-dimensional images of the measuring volume are simultaneously generated on the detector surfaces. The detectors “observe” the measuring volume at different observation angles. Usually, each detector has its own optics. However, since the specific configuration of the optics does not play a role in the present description, the term “detection optics” will be used here to include any optical entity with which the measuring volume is imaged onto the detector surfaces.
Depending on the specific measuring method, the images recorded are used to reconstruct either the individual particle constellation in the volume (3D-PTV) or the voxel-wise intensity distribution of the measuring volume (tomographic PIV; see, for example, EP 1 517 150 B1).
The recording of the image, with subsequent reconstruction, is carried out at least twice at different measuring times. Comparison of the reconstructions provides information on the flow-related shifts that have occurred between the two measuring times. Together with the knowledge of the time interval that has elapsed between the measuring points, it is possible from this to reconstruct a velocity field that represents the flow in the measuring volume.
In order to reconstruct the particle constellation or the voxel-wise intensity distribution in the measuring volume by using the recorded images of the measuring volume, it is necessary to know very precisely how a volume position in the measuring volume is imaged onto an image position on a detector surface. This relationship is described by the so-called imaging function. In particular, the imaging function assigns an image position (xi, yi) on an i-th detector surface to each volume position (X, Y, Z) in the measuring volume. Typically, its own imaging function is formulated for each detector, which is why in the context of the present description reference will be made to a set of imaging functions. However, this should also explicitly include situations in which the imaging functions of individual detectors are grouped together, for example in matrix notation, to give an overall imaging function.
The imaging function is typically unique, i.e. exactly one image position on the corresponding detector surface is assigned to each volume position in the measuring volume. However, the reversal of the imaging function is as a rule not unique. In particular, all volume positions on the “line of sight” of a detector are imaged on the same image position of its detector surface. The reversal of the imaging function thus assigns an entire group of volume positions in the measuring volume to individual image positions on the corresponding detector surface.
In order, nevertheless, to arrive at a unique reconstruction, the information of several images is jointly evaluated in a so-called triangulation method. In particular, the reversals of the imaging functions can be applied to the images of an individually identified particle on different detector surfaces. Then, that volume position which is common to all the groups of volume positions which are assigned to the image positions of the particle can be determined as the volume position of the particle. This leads to an overdetermined result even when only two detectors are used. Typically, however, three and more detectors are used, so that a significant overdetermination exists. Due to measuring inaccuracies, this means that the sight lines of the detectors calculated from the particle images do not intersect exactly at a common point. This is the typical situation that arises, in particular when the imaging functions are determined solely by coarse calibration, e.g. using a calibration plate.
As a remedy, the above-mentioned generic German Patent DE 10 2006 055 746 A1 proposes improving the imaging functions. This type of improvement has in the meantime become known in technical circles under the name of “volume self-calibration”. In the case of volume self-calibration the volume position of the particle is initially only approximately determined by triangulation. Correction factors for the imaging functions are then calculated, depending on the relative location of the approximately determined volume position of the lines of sight of the detectors predetermined by the imaging functions. Next, triangulation is again carried out with the corrected imaging functions and the volume position is again approximately determined. This procedure is usually iteratively performed until suitable correction factors for the imaging functions are found, in order to determine the volume position of the particle with sufficient accuracy, i.e. within a predetermined tolerance. The improved imaging functions determined in this way are used as the basis for the further procedure—whether it is a PIV or a PTV method.
It is a disadvantage of the known method that, although an improved geometrical assignment of volume points and image points is achieved, other imaging errors however are completely ignored. In particular, imaging errors that are caused by defocusing, spherical aberration or astigmatism of the detection optics are not considered at all. The greater the size of the imaged measuring volume, the more significant such imaging errors become. In particular when carrying out flow analysis of large components, such imaging errors can have a considerable influence on the measuring result.
It is the problem of the present invention to further develop a generic method in such a way that complex imaging errors can be compensated for.